A dynamic model for the time evolution of the modulated cosmic ray spectrum
Abstract
A recently developed model predicts an energy dependent phase lag in the modulated cosmic ray density U at time t given by U(t) ≃ U_{s}(t  τ), where U_{s} is the solution to the FokkerPlanck equation under time independent conditions and τ is the average time spent by particles inside the modulating region. The delay times τ are functions of modulating parameters R (the radius of the modulating cavity), V (the solar wind velocity), and K (the effective average diffusion coefficient which is a function of energy). This model is applied to predict the time evolution of the modulated cosmic ray proton spectrum over a simulated solar cycle. The predicted spectra reproduce most of the features of the socalled hysteresis effect when values of V = 360 km/s, R = 60 AU, and K varying between 1.3 × 10^{22} cm²/s at solar maximum and 3.5 × 10^{22} cm²/s at solar minimum are used. A modulation produced mostly by varying R over the solar cycle is less consistent with the observations.
 Publication:

Journal of Geophysical Research
 Pub Date:
 March 1976
 DOI:
 10.1029/JA081i007p01319
 Bibcode:
 1976JGR....81.1319O
 Keywords:

 Energy Spectra;
 Galactic Radiation;
 Modulated Continuous Radiation;
 Primary Cosmic Rays;
 Solar Cycles;
 Solar Wind Velocity;
 Astronomical Models;
 Dynamic Models;
 Long Term Effects;
 Magnetic Rigidity;
 Phase Shift;
 Solar Protons;
 Space Radiation;
 Particles and FieldsInterplanetary Space: Cosmic rays